Decision criteria, statistical

Direction of innovation tfrom the standpoint of market actors - 6al Automotive manufacturers substantiate the reduction of solvent emissions by water-based and powdered coatings on the basis of emission statistics. However, the automotive manufacturers state the improvement of the surface quality with the simultaneous improved cost-effectiveness of procedures as the decisive criterion for successful innovation. 

On the subject of nomenclature, a word concerning historically used terms for the detection decision point or level Is in order. As stated Immediately above, a number of analysts, following Kaiser, use "Limit of Detection" or "Detection Limit" as both the measure of (true concentration) detection capability and as a statistical critical level or threshold to make detection decisions. Following established practice in Statistics, the term "Critical Level" was recommended in (23 ). "Criterion of Detection" has been employed by Wilson (22) > Liteanu (8), who speaks of the "decision criterion" as a strategy, terms the numerical comparison level the "Decision (or Detection) Threshold."... 

Both hypothesis statements reflect the same objective, but there are significant differences in the decision criterion utilized in each hypothesis. The null hypothesis of case I assumes that the well is producing 100 or more barrels per day unless statistical evidence proves otherwise, resulting in rejection of Hq. The null hypothesis of case II assumes that the well production is inferior unless production records indicate that daily output is more than 100 barrels per day, which will result in rejection of Hq. Both tests are valid and are called one-tailed hypothesis tests under a given type I error. Consider again the original data with a = 0.05. Table 3 summarizes the calculations for the significance tests associated with cases I and II. 

The previous subsections were primarily concerned with the behavior of the three-frequency nonlinear heterodyne system for applications in cw radar and analog communications. As such, a determination of the output signal-to-noise ratio (SNR)o was adequate to characterize the system. In this subsection, we investigate applications in digital communications and pulsed radar, and therefore examine system performance in terms of the error probability P. Evaluation of the probability of error under various conditions requires a decision criterion as well as a knowledge of the signal statistics we now investigate operation of the three-frequency nonlinear heterodyne scheme in the time domain rather than in the frequency domain. 

There are several statistical tests for reaching such a decision, the most popular probably being the "Chauvenet" criterion. Application of this criterion here uses the results shown in figure 7. 

Once the list is culled, a decision must be made on how to score each criterion. This can be as simple as a qualitative judgment of effectiveness (+), ineffectiveness (—), or indifference ( ), or a simple subjective score (say, 1 to 10). Some criteria lend themselves to a more quantitative evaluation of a relevant statistic, such as expected profit, volume, sales, and so on. Once the choices are made, each altemative solution can then be rated according to the list of criteria. 

Sometimes, a value within a set might appear aberrant (this is known as an outlier). Although it might be tempting to reject this data point, it must be remembered that a value can only be aberrant relative to some law of probability. There is a simple statistical criterion on which to base the decision of whether to retain or reject this value. Dixon s test is based on the following ratio (as long as there are at least seven measurements) ... 

In Sections 2 to 4, we review the technology of synthetic oligonucleotide microarrays and describe some of the popular statistical methods that are used to discover genes with differential expression in simple comparative experiments. A novel Bayesian procedure is introduced in Section 5 to analyze differential expression that addresses some of the limitations of current procedures. We proceed, in Section 6, by discussing the issue of sample size and describe two approaches to sample size determination in screening experiments with microarrays. The first approach is based on the concept of reproducibility, and the second approach uses a Bayesian decision-theoretic criterion to trade off information gain and experimental costs. We conclude, in Section 7, with a discussion of some of the open problems in the design and analysis of microarray experiments that need further research. 

Interpretation of the control data is guided by certain decision criteria or control rules, which define when an analytical run is judged in control (acceptable) or out of control (unacceptable). These control rules are given symbols, such as At, or tii, where A is the abbreviation for a statistic n is the number of control observations, and L refers to the control limits. For example, Gs refers to a control rule where 1 observation exceeding the mean +3s control limits is the criterion for rejecting the analytical run. 

As for immunoassays for pharmaceutical proteins, in-study validation of biomarker assays should include one set of calibrators to monitor the standard curve as well as a set of QC samples at three concentrations analyzed in duplicate for the decision to accept or reject a specific run. Recommended acceptance criterion is the 6-4-30 rule, but even more lenient acceptance criteria may be justified based on statistical rationale developed from experimental data [14]. 

When the uncertainty in the parameter values becomes too large, the analyst should consider reducing the model. The correlation matrix between parameters can be useful in selecting the parameters that can be removed to make the model smaller. There are statistical criteria that can be used to select the better model. These include the Akaike Information Criterion (AIC) value and the F-test. The AIC value is calculated using the WSS, the number of parameters in the model, and the number of data points. The model with the lower AIC values is usually selected as the better model. The statistical F-test involves the calculation of an F value from the WSS and degrees of freedom from two analyses. The calculated F value is compared with the tabled values and a decision can be made whether the more complex model provides a significant improvement in the fit to the data. The analyst using a combination of subjective and objective criteria can make an educated decision about the best model. 

A statistical test provides a mechanism for making quantitative decisions about a set of data. Any statistical test for the evaluation of quantitative data involves a mathematical model for the theoretical distribution of the experimental measurements (reflecting the precision of the measurements), a pair of competing hypotheses and a user-selected criterion (e.g., the confidence level) for making a decision concerning the validity of any specific hypothesis. All hypothesis tests address uneertainty in the results by attempting to refute a specific claim made about the results based on the data set itself. 

The criterion characterizes a modeling technique used to solve the supply chain configuration problem. Analysis of this criterion reveals the most often used techniques. Values of the criterion include different methods of mathematical programming, simulation, statistical analysis, data modeling, and hybrid techniques. Usually, one method is indicated unless several methods having similar importance to decision-making are used. 

If the standard deviation is known, the probability for any measuring value to be either a blank value or a part of an existing compound amount can be calculated statistically. As a criterion for this decision, the error probability is used ... 

Much of the early success of density functional theory is due to the success in the description of the band structure of the crystals. However, a quantitative agreement is still missing all existing density fimctional approximations produce errors which are larger than the (assumed) experimental error bars. In this paper, we analyze whether statistical descriptors of the errors in the calculated band gaps allow choosing the best approximation. It is shown that different measures recommend different approximations. We thus conclude that faced with such a dilemma, in order to make a decision, one is coerced into using some additional, external criterion. 

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